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<td class="title">Thinning And Thickening</td>
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<h1>mmcwatershed
<br>
<span class="subtitle">Detection of watershed from markers.
</span>
</h1>
<div class="synopsis">
<H2>Synopsis</H2>
<div class="H2">
<div class="prototype">Y =
<span class="fun">mmcwatershed</span>(
<span class="par">f</span>,
<span class="par">g</span>,
<span class="par">Bc</span> = None,
<span class="par">LINEREG</span> = "LINES"
)
</div>
<p>Implemented in
<b>Python.</b>
</p>
<div class="input">
<H3>Input</H3>
<div class="H3">
<table class="deflist">
<tbody valign="baseline">
<tr>
<td class="term"><span class="par">f</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmImage.html">Image</a></span> Gray-scale (uint8 or uint16) image.
</td>
</tr>
<tr>
<td class="term"><span class="par">g</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmImage.html">Image</a></span> Gray-scale (uint8 or uint16) or binary image.
<p>marker image: binary or labeled.</p></td>
</tr>
<tr>
<td class="term"><span class="par">Bc</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmSe.html">Structuring Element</a></span><p>(watershed connectivity)</p><p>Default:
<code>None</code> (3x3 elementary cross)
</p></td>
</tr>
<tr>
<td class="term"><span class="par">LINEREG</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmString.html">String</a></span><p>'LINES' or ' REGIONS'.</p><p>Default:
<code>"LINES"</code>
</p></td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="output">
<H3>Output</H3>
<div class="H3">
<table class="deflist">
<tbody valign="baseline">
<tr>
<td class="term"><span class="par">Y</span></td>
<td class="def"><span class="type"><a href="../mmtypes/mmImage.html">Image</a></span> Gray-scale (uint8 or uint16) or binary image.
</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</div>
<div class="descr">
<H2>Description</H2>
<div class="H2">
<p>
<span class="fun">mmcwatershed</span> creates the image
<code>y</code> by detecting the domain of the catchment basins of
<code>f</code> indicated by the marker image
<code>g</code>, according to the connectivity defined by
<code>Bc</code>. According to the flag LINEREG
<code>y</code> will be a labeled image of the catchment basins domain or just a binary image that presents the watershed lines. To know more about watershed and watershed from markers, see BeucMeye:93. The implementation of this function is based on LotuFalc:00. WARNING: There is a common mistake related to the marker image
<code>g</code>. If this image contains only zeros and ones, but it is not a binary image, the result will be an image with all ones. If the marker image is binary, you have to set this explicitly using the
<code>logical</code> function.
</p>
</div>
</div>
<div class="examples">
<H2>Examples</H2>
<div class="H2">
<p>
<div class="example">
<div class="listing">
<pre class="user">>>> a = uint8([\
[10, 10, 10, 10, 10, 10, 10],\
[10, 9, 6, 18, 6, 5, 10],\
[10, 9, 6, 18, 6, 8, 10],\
[10, 9, 9, 15, 9, 9, 10],\
[10, 9, 9, 15, 12, 10, 10],\
[10, 10, 10, 10, 10, 10, 10]])</pre>
<pre class="computer"></pre>
<pre class="user">>>> b = mmcmp(a,'==',uint8(6))</pre>
<pre class="computer"></pre>
<pre class="user">>>> print mmcwatershed(a,b)</pre>
<pre class="computer">[[0 0 0 1 0 0 0]
[0 0 0 1 0 0 0]
[0 0 0 1 0 0 0]
[0 0 0 1 0 0 0]
[0 0 0 1 0 0 0]
[0 0 0 0 1 0 0]]</pre>
<pre class="user">>>> print mmcwatershed(a,b,mmsecross(),'REGIONS')</pre>
<pre class="computer">[[1 1 1 1 2 2 2]
[1 1 1 1 2 2 2]
[1 1 1 1 2 2 2]
[1 1 1 1 2 2 2]
[1 1 1 1 2 2 2]
[1 1 1 1 2 2 2]]</pre>
</div>
</div>
<div class="example">
<div class="listing">
<pre class="user">>>> f=mmreadgray('astablet.tif')</pre>
<pre class="computer"></pre>
<pre class="user">>>> grad=mmgradm(f)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mark=mmregmin(mmhmin(grad,17))</pre>
<pre class="computer"></pre>
<pre class="user">>>> w=mmcwatershed(grad,mark)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(grad)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(mark)</pre>
<pre class="computer"></pre>
<pre class="user">>>> mmshow(w)</pre>
<pre class="computer"></pre>
</div>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="251" src="../images/img_mmcwatershed_001.jpg"></td>
<td><img width="251" src="../images/img_mmcwatershed_002.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmcwatershed_001.jpg">grad</a></td>
<td><a href="../images/img_mmcwatershed_002.jpg">mark</a></td>
<td class="spare"></td>
</tr>
</tbody>
</table>
<table class="images">
<tbody align="center">
<tr class="image" valign="bottom">
<td><img width="251" src="../images/img_mmcwatershed_003.jpg"></td>
<td class="spare"></td>
</tr>
<tr class="title" valign="baseline">
<td><a href="../images/img_mmcwatershed_003.jpg">w</a></td>
<td class="spare"></td>
</tr>
</tbody>
</table>
</div>
</p>
</div>
</div>
<div class="equation">
<H2>Equation</H2>
<div class="H2">
<p>
<div class="bridge">Equation (watershed regions):</div>
<div class="eqfig">
<img src="../images/eq_mmcwatershed001.png">
</div>
<div class="bridge">Minimum length of a point to a set:</div>
<div class="eqfig">
<img src="../images/eq_mmcwatershed002.png">
</div>
<div class="bridge">Length of a point to a set:</div>
<div class="eqfig">
<img src="../images/eq_mmcwatershed003.png">
</div>
<div class="bridge">Where:</div>
<div class="eqfig">
<img src="../images/eq_mmcwatershed004.png">
</div>is the path between the point
<i>x</i> and subset
<i>X</i> under connectivity
<i>Bc</i>
</p>
</div>
</div>
<div class="sourcecode">
<H2>Source Code</H2>
<div class="H2">
<pre class="listing">
def mmcwatershed(f, g, Bc=None, LINEREG="LINES"):
from Numeric import ones, zeros, nonzero, array, put, take, argmin, transpose, compress, concatenate
if Bc is None: Bc = mmsecross()
return g
print 'starting'
withline = (LINEREG == 'LINES')
if mmis(g,'binary'):
g = mmlabel(g,Bc)
print 'before 1. mmpad4n'
status = mmpad4n(uint8(zeros(f.shape)),Bc, 3)
f = mmpad4n( f,Bc,0) #pad input image
print 'before 2. mmpad4n'
y = mmpad4n( g,Bc,0) # pad marker image with 0
if withline:
y1 = mmintersec(mmbinary(y), 0)
costM = mmlimits(f)[1] * ones(f.shape) # cummulative cost function image
mi = nonzero(mmgradm(y,mmsebox(0),Bc).flat) # 1D index of internal contour of marker
print 'before put costM'
put(costM.flat,mi, 0)
HQueue=transpose([mi, take(costM.flat, mi)]) # init hierarquical queue: index,value
print 'before mmse2list0'
Bi=mmse2list0(f,Bc) # get 1D displacement neighborhood pixels
x,v = mmmat2set(Bc)
while HQueue:
print 'Hq=',HQueue
i = argmin(HQueue[:,1]) # i is the index of minimum value
print 'imin=',i
pi = HQueue[i,0]
print 'pi=',pi
ii = ones(HQueue.shape[0])
ii[i] = 0
print 'ii=',ii
HQueue = transpose(array([compress(ii,HQueue[:,0]),
compress(ii,HQueue[:,1])])) # remove this pixel from queue
print 'H=',HQueue
put(status.flat, pi, 1) # make it a permanent label
for qi in pi+Bi : # for each neighbor of pi
if (status.flat[qi] != 3): # not image border
if (status.flat[qi] != 1): # if not permanent
cost_M = max(costM.flat[pi], f.flat[qi])
if cost_M < costM.flat[qi]:
print 'qi=',qi
costM.flat[qi] = cost_M
y.flat[qi] = y.flat[pi] # propagate the label
aux = zeros(array(HQueue.shape) + [1,0])
aux[:-1,:] = HQueue
aux[-1,:]=[qi, cost_M]
HQueue = aux # insert pixel in the queue
print 'insert H=',HQueue
elif (withline and
(y.flat[qi] != y.flat[pi]) and
(y1.flat[pi] == 0) and
(y1.flat[qi] == 0) ):
y1.flat[pi] = 1
if withline:
Y = y1
else:
Y = y
return Y
</pre>
</div>
</div>
<div class="seealso">
<H2>See also</H2>
<div class="H2">
<table class="deflist">
<tbody valign="baseline">
<tr>
<td class="term"><a href="../morph/mmfreedom.html">mmfreedom</a></td>
<td class="def">Control automatic data type conversion.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmwatershed.html">mmwatershed</a></td>
<td class="def">Watershed detection.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmsebox.html">mmsebox</a></td>
<td class="def">Create a box structuring element.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmsecross.html">mmsecross</a></td>
<td class="def">Diamond structuring element and elementary 3x3 cross.</td>
</tr>
<tr>
<td class="term"><a href="../morph/mmswatershed.html">mmswatershed</a></td>
<td class="def">Detection of similarity-based watershed from markers.</td>
</tr>
<tr>
<td class="term"><a href="../mmdemos/mmdcalc.html">mmdcalc</a></td>
<td class="def">Extract the keys of a calculator.</td>
</tr>
</tbody>
</table>
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<td class="copyright">Copyright (c) 2003, Roberto A. Lotufo, UNICAMP-University of Campinas; Rubens C. Machado, CenPRA-Renato Archer Research Center.</td>
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distrib
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Mandriva
>
2010.0
>
i586
>
media
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contrib-release
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by-pkgid
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